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Rostyslav Hryniv

Publications and source records attributed to Rostyslav Hryniv.

12 recordsLinked to original sources
arXiv2026

Scattering in Quantum Graphs with Scale-Invariant Vertex Couplings: Resonances, Gaps and (Quasi-)Periodic Transmission

We study scattering on quantum graphs that consist of a channel with periodically attached resonators under scale-invariant vertex couplings. For this model, we derive explicit formulas for the transmission probability and analyse how it depends on the geometric and coupling parameters. Contrary to standard one-dimensional scattering, where the potential barrier becomes transparent at high energy, here the transmission probability does not approach unity; instead, it is periodic or quasi-periodic, with infinitely many energies of complete reflection and of perfect transmission persisting at arbitrarily high energy. We further show that the model exhibits strong transmission suppression near the anti-resonant frequencies, resulting in pronounced spectral gaps. The width and structure of these gaps depend on the number of resonators and the coupling parameters. As a result, such quantum graphs can be used to engineer transport properties and to tune spectral filtering.

math.SP↗
arXiv2026

Ukrainian Visual Word Sense Disambiguation Benchmark

This study presents a benchmark for evaluating the Visual Word Sense Disambiguation (Visual-WSD) task in Ukrainian. The main goal of the Visual-WSD task is to identify, with minimal contextual information, the most appropriate representation of a given ambiguous word from a set of ten images. To construct this benchmark, we followed a methodology similar to that proposed by (CITATION), who previously introduced benchmarks for the Visual-WSD task in English, Italian, and Farsi. This approach allows us to incorporate the Ukrainian benchmark into a broader framework for cross-language model performance comparisons. We collected the benchmark data semi-automatically and refined it with input from domain experts. We then assessed eight multilingual and multimodal large language models using this benchmark. All tested models performed worse than the zero-shot CLIP-based baseline model (CITATION) used by (CITATION) for the English Visual-WSD task. Our analysis revealed a significant performance gap in the Visual-WSD task between Ukrainian and English.

cs.CV↗
arXiv2025

Transmission resonances in scattering by $δ'$-like combs

We introduce a new exactly solvable model in quantum mechanics that describes the propagation of particles through a potential field created by regularly spaced $δ'$-type point interactions, which model the localized dipoles often observed in crystal structures. We refer to the corresponding potentials as $δ'_θ$-combs, where the parameter $θ$ represents the contrast of the resonant wave at zero energy and determines the interface conditions in the Hamiltonians. We explicitly calculate the scattering matrix for these systems and prove that the transmission probability exhibits sharp resonance peaks while rapidly decaying at other frequencies. Consequently, Hamiltonians with $δ'_θ$-comb potentials act as quantum filters, permitting tunnelling only for specific wave frequencies. Furthermore, for each $θ> 0$, we construct a family of regularized Hamiltonians approximating the ideal model and prove that their transmission probabilities have a similar structure, thereby confirming the physical realizability of the band-pass filtering effect.

math.SP↗
arXiv2025

On negative eigenvalues of 1D Schrödinger operators with $δ'$-like potentials

In this paper, we investigate negative eigenvalues of exactly solvable quantum models, particularly one-dimensional Hamiltonians with $δ'$-like potentials used to represent localized dipoles. These operators arise as norm resolvent limits of Schrödinger operators with suitably regularized potentials. Although the limiting operator is bounded below, we show that the approximating operators may possess a finite but arbitrarily large number of negative eigenvalues that diverge to $-\infty$ as the regularization parameter vanishes. This phenomenon illustrates a spectral instability of Schrödinger operators with $δ'$-like singularities.

math.SP↗
arXiv2022

Towards realistic symmetry-based completion of previously unseen point clouds

3D scanning is a complex multistage process that generates a point cloud of an object typically containing damaged parts due to occlusions, reflections, shadows, scanner motion, specific properties of the object surface, imperfect reconstruction algorithms, etc. Point cloud completion is specifically designed to fill in the missing parts of the object and obtain its high-quality 3D representation. The existing completion approaches perform well on the academic datasets with a predefined set of object classes and very specific types of defects; however, their performance drops significantly in the real-world settings and degrades even further on previously unseen object classes. We propose a novel framework that performs well on symmetric objects, which are ubiquitous in man-made environments. Unlike learning-based approaches, the proposed framework does not require training data and is capable of completing non-critical damages occurring in customer 3D scanning process using e.g. Kinect, time-of-flight, or structured light scanners. With thorough experiments, we demonstrate that the proposed framework achieves state-of-the-art efficiency in point cloud completion of real-world customer scans. We benchmark the framework performance on two types of datasets: properly augmented existing academic dataset and the actual 3D scans of various objects.

cs.CV↗
arXiv2020

Minimal Solvers for Single-View Lens-Distorted Camera Auto-Calibration

This paper proposes minimal solvers that use combinations of imaged translational symmetries and parallel scene lines to jointly estimate lens undistortion with either affine rectification or focal length and absolute orientation. We use constraints provided by orthogonal scene planes to recover the focal length. We show that solvers using feature combinations can recover more accurate calibrations than solvers using only one feature type on scenes that have a balance of lines and texture. We also show that the proposed solvers are complementary and can be used together in a RANSAC-based estimator to improve auto-calibration accuracy. State-of-the-art performance is demonstrated on a standard dataset of lens-distorted urban images. The code is available at https://github.com/ylochman/single-view-autocalib.

cs.CV↗
arXiv2020

Inverse scattering on the half-line for energy-dependent Schrödinger equations

In this paper, we study the inverse scattering problem for energy-dependent Schrödinger equations on the half-line with energy-dependent boundary conditions at the origin. Under certain positivity and very mild regularity assumptions, we transform this scattering problem to the one for non-canonical Dirac systems and show that, in turn, the latter can be placed within the known scattering theory for ZS-AKNS systems. This allows us to give a complete description of the corresponding scattering functions S for the class of problems under consideration and justify an algorithm of reconstructing the problem from S

math.SP↗
arXiv2020

Spectra of rank-one perturbations of self-adjoint operators

We characterize possible spectra of rank-one perturbations B of a self-adjoint operator A with discrete spectrum and, in particular, prove that the spectrum of B may include any number of real or non-real eigenvalues of arbitrary algebraic multiplicity

math.SP↗
arXiv2012

Inverse spectral problems for energy-dependent Sturm-Liouville equations

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.

math.SP↗